Arising from structural graph theory, treewidth has become a focus of study in fixed-
parameter tractable algorithms. Many NP-hard problems are known to be solvable in O (n· 2 …

Explaining the excellent practical performance of the simplex method for linear programming
has been a major topic of research for over 50 years. One of the most successful frameworks …

Many algorithms use data structures that maintain properties of matrices undergoing some
changes. The applications are wide-ranging and include for example matchings, shortest …

Circuit-augmentation algorithms are generalizations of the simplex method, where in each
step one is allowed to move along a fixed set of directions, called circuits, that is a superset …

We present three new pivot rules for the Simplex method for Linear Programs over 0/1-
polytopes. We show that the number of nondegenerate steps taken using these three rules …

Chazelle and Matoušek [J. Algorithms, 1996] presented a derandomization of Clarkson's
sampling-based algorithm [J. ACM, 1995] for solving linear programs with n constraints and …

We consider the computational problem of finding short paths in the skeleton of the perfect
matching polytope of a bipartite graph. We prove that unless P= NP, there is no polynomial …

The question whether the Simplex Algorithm admits an efficient pivot rule remains one of the
most important open questions in discrete optimization. While many natural, deterministic …

A general issue in computational optimization is to develop combinatorial algorithms for
semidefinite programming. We address this issue when the base field is nonarchimedean …

We present an improved exponential time algorithm for Energy Games, and hence also for
Mean Payoff Games. The running time of the new algorithm is O (min (mn W, mn 2^{n/2} log …